Dumb MMA/UFC question

Just a random thought I was curious about ... Jiujitsu, wrestling and boxing seem to be the dominant styles of fighting in MMA matches, but are people obligated to use those by rule or has the sport just evolved to the point where it's accepted those are the most effective tactics? If you had a different martial art that you could be effective with, would you be allowed to use it?
Like, if the Monkey-Fu guy from Bloodsport or an actual ninja showed up in UFC and started kicking everyone's ass with their crazy moves, would that be permissible?

It's the evolution. Generally, the tactic is that if you try anything to crazy in terms of flying kicks or other ninja move, you're open to getting KO'd on the counter or tackled/controlled by a wrestler.